## Volume functions on blow-ups and Seshadri constants

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- by François Ballaÿ PDF
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**150**(2022), 1925-1935 Request permission

## Abstract:

We exhibit some relations between the Seshadri constant of an ample divisor along a closed subscheme and the behaviour of the volume function on the corresponding blow-up. As an application, we give an equivalent formulation of Nagata’s conjecture in terms of the differentiability of a real valued function.## References

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## Additional Information

**François Ballaÿ**- Affiliation: Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France
- Email: francois.ballay@uca.fr
- Received by editor(s): April 15, 2021
- Received by editor(s) in revised form: August 3, 2021, and August 11, 2021
- Published electronically: February 18, 2022
- Communicated by: Rachel Pries
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**150**(2022), 1925-1935 - MSC (2020): Primary 14C20
- DOI: https://doi.org/10.1090/proc/15803
- MathSciNet review: 4392328